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Simplifying 8n2 = 64n + -128 Reorder the terms: 8n2 = -128 + 64n Solving 8n2 = -128 + 64n Solving for variable 'n'. Reorder the terms: 128 + -64n + 8n2 = -128 + 64n + 128 + -64n Reorder the terms: 128 + -64n + 8n2 = -128 + 128 + 64n + -64n Combine like terms: -128 + 128 = 0 128 + -64n + 8n2 = 0 + 64n + -64n 128 + -64n + 8n2 = 64n + -64n Combine like terms: 64n + -64n = 0 128 + -64n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(16 + -8n + n2) = 0 Factor a trinomial. 8((4 + -1n)(4 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {4, 4}
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